Invariants
Level: | $304$ | $\SL_2$-level: | $16$ | ||||
Index: | $96$ | $\PSL_2$-index: | $48$ | ||||
Genus: | $0 = 1 + \frac{ 48 }{12} - \frac{ 0 }{4} - \frac{ 0 }{3} - \frac{ 10 }{2}$ | ||||||
Cusps: | $10$ (none of which are rational) | Cusp widths | $2^{8}\cdot16^{2}$ | Cusp orbits | $2^{3}\cdot4$ | ||
Elliptic points: | $0$ of order $2$ and $0$ of order $3$ | ||||||
$\Q$-gonality: | $1 \le \gamma \le 2$ | ||||||
$\overline{\Q}$-gonality: | $1$ | ||||||
Rational cusps: | $0$ | ||||||
Rational CM points: | none |
Other labels
Cummins and Pauli (CP) label: | 16G0 |
Level structure
$\GL_2(\Z/304\Z)$-generators: | $\begin{bmatrix}187&260\\274&273\end{bmatrix}$, $\begin{bmatrix}215&48\\291&161\end{bmatrix}$, $\begin{bmatrix}283&0\\155&253\end{bmatrix}$, $\begin{bmatrix}291&220\\222&185\end{bmatrix}$ |
Contains $-I$: | no $\quad$ (see 304.48.0.f.1 for the level structure with $-I$) |
Cyclic 304-isogeny field degree: | $40$ |
Cyclic 304-torsion field degree: | $5760$ |
Full 304-torsion field degree: | $31518720$ |
Models
This modular curve is isomorphic to $\mathbb{P}^1$.
Rational points
This modular curve has real points and $\Q_p$ points for $p$ not dividing the level, but no known rational points.
Modular covers
This modular curve minimally covers the modular curves listed below.
Covered curve | Level | Index | Degree | Genus | Rank |
---|---|---|---|---|---|
8.48.0-8.k.1.5 | $8$ | $2$ | $2$ | $0$ | $0$ |
304.48.0-304.f.1.2 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-304.f.1.29 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-304.f.2.6 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-304.f.2.19 | $304$ | $2$ | $2$ | $0$ | $?$ |
304.48.0-8.k.1.1 | $304$ | $2$ | $2$ | $0$ | $?$ |
This modular curve is minimally covered by the modular curves in the database listed below.
Covering curve | Level | Index | Degree | Genus |
---|---|---|---|---|
304.192.1-304.t.1.4 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.t.2.8 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.w.1.3 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.w.2.7 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.ba.1.2 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.ba.2.4 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.bd.1.1 | $304$ | $2$ | $2$ | $1$ |
304.192.1-304.bd.2.3 | $304$ | $2$ | $2$ | $1$ |